Finite Group Databasebeta

← Group #11723008

Character table — Group #11723008

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222224444444444446666666666668888121212121212121212121212121212121212121212181818181818363636363636108
order1222333666666666333666666666444412121212121212123666266666666121212121212121212121212441212121244121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1
χ4111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111-1-111-1-1-1-111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1
χ61111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-111-1-11
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ9222222-12-1222-122-12-1-122-1-1-1-1-12-1002200002222-1-1-1-1222-1-1-1-1-1-100-1-10000-1-1-1-10000000200-1-10
χ10222222-12-1222-122-12-1-122-1-1-1-1-12-1002200002222-1-1-1-1-2-2-211111100-1-10000-1-1-1-10000000-200110
χ11222222-12-1222-122-12-1-122-1-1-1-1-12-100-2-20000-2-2-2-2-1-1-1-1222-1-1-1-1-1-10011000011110000000-200110
χ12222222-12-1222-122-12-1-122-1-1-1-1-12-100-2-20000-2-2-2-2-1-1-1-1-2-2-21111110011000011110000000200-1-10
χ1322222-12-1222-122-12-12-1-1-122-1-1-1-12220022220000-1-1-1-12-1-122-1-1-1-1-1-100-1-1-1-1000000000020-1-1000
χ1422222-12-1222-122-12-12-1-1-122-1-1-1-12220022220000-1-1-1-1-211-2-21111-1-100-1-1-1-10000000000-2011000
χ1522222-12-1222-122-12-12-1-1-122-1-1-1-12-2-200-2-2-2-20000-1-1-1-12-1-122-1-1-1-1110011110000000000-2011000
χ1622222-12-1222-122-12-12-1-1-122-1-1-1-12-2-200-2-2-2-20000-1-1-1-1-211-2-2111111001111000000000020-1-1000
χ172222-12222-1-122-122-1-12-1-1-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000002222-1-1-1-1-1-1-1-122-1-1-1-10000000
χ182222-12222-1-122-122-1-12-1-1-1-1222-1-122-2-2-1-1-1-11111-1-1-1-100000000022-2-2-1-1-1-11111-2-211110000000
χ192222-12222-1-122-122-1-12-1-1-1-1222-1-1-2-2221111-1-1-1-1-1-1-1-1000000000-2-2221111-1-1-1-1-2-211110000000
χ202222-12222-1-122-122-1-12-1-1-1-1222-1-1-2-2-2-211111111-1-1-1-1000000000-2-2-2-21111111122-1-1-1-10000000
χ2122-2-22222-22-2-22-2-2-22222-2-2-22-2-2-222i−2i002i2i−2i−2i000022-2-20000000002i−2i002i2i−2i−2i00000000000000000
χ2222-2-22222-22-2-22-2-2-22222-2-2-22-2-2-22−2i2i00−2i−2i2i2i000022-2-2000000000−2i2i00−2i−2i2i2i00000000000000000
χ2322-2-22-12-1-22-212-21-2-12-1-11-2-2-111122i−2i002i2i−2i−2i0000-1-1110−i3i300−i3−i3i3i3−ii00−i−iii0000000000003−3000
χ2422-2-22-12-1-22-212-21-2-12-1-11-2-2-111122i−2i002i2i−2i−2i0000-1-1110i3−i300i3i3−i3−i3−ii00−i−iii000000000000−33000
χ2522-2-22-12-1-22-212-21-2-12-1-11-2-2-11112−2i2i00−2i−2i2i2i0000-1-1110−i3i300−i3−i3i3i3i−i00ii−i−i000000000000−33000
χ2622-2-22-12-1-22-212-21-2-12-1-11-2-2-11112−2i2i00−2i−2i2i2i0000-1-1110i3−i300i3i3−i3−i3i−i00ii−i−i0000000000003−3000
χ2722-2-2-1222-2-11-221-2-2-1-12-11112-2-21-12i−2i00−i−iii−i3−i3i3i3-1-1110000000002i−2i00−i−iii−i3−i3i3i30033−3−30000000
χ2822-2-2-1222-2-11-221-2-2-1-12-11112-2-21-12i−2i00−i−iiii3i3−i3−i3-1-1110000000002i−2i00−i−iiii3i3−i3−i300−3−3330000000
χ2922-2-2-1222-2-11-221-2-2-1-12-11112-2-21-1−2i2i00ii−i−i−i3−i3i3i3-1-111000000000−2i2i00ii−i−i−i3−i3i3i300−3−3330000000
χ3022-2-2-1222-2-11-221-2-2-1-12-11112-2-21-1−2i2i00ii−i−ii3i3−i3−i3-1-111000000000−2i2i00ii−i−ii3i3−i3−i30033−3−30000000
χ312-22-2222-22-222-2-2-2-2222-2-22-2-22-22-2002i−2i00002i−2i2i−2i2-22-2000000000002i−2i00002i−2i2i−2i0000000000000
χ322-22-2222-22-222-2-2-2-2222-2-22-2-22-22-200−2i2i0000−2i2i−2i2i2-22-200000000000−2i2i0000−2i2i−2i2i0000000000000
χ332-22-222-1-2-1-2221-2-212-1-1-2-2-111-1121002i−2i00002i−2i2i−2i-11-11000−i3i3−i3i3−i3i300−ii0000−ii−ii00000000003−30
χ342-22-222-1-2-1-2221-2-212-1-1-2-2-111-1121002i−2i00002i−2i2i−2i-11-11000i3−i3i3−i3i3−i300−ii0000−ii−ii0000000000−330
χ352-22-222-1-2-1-2221-2-212-1-1-2-2-111-112100−2i2i0000−2i2i−2i2i-11-11000−i3i3−i3i3−i3i300i−i0000i−ii−i0000000000−330
χ362-22-222-1-2-1-2221-2-212-1-1-2-2-111-112100−2i2i0000−2i2i−2i2i-11-11000i3−i3i3−i3i3−i300i−i0000i−ii−i00000000003−30
χ372-22-2-122-221-12-21-2-2-1-1211-11-22-2-11002i−2i−i3i3−i3i3−ii−ii-11-11000000000002i−2i−i3i3−i3i3−ii−ii003−33−30000000
χ382-22-2-122-221-12-21-2-2-1-1211-11-22-2-11002i−2ii3−i3i3−i3−ii−ii-11-11000000000002i−2ii3−i3i3−i3−ii−ii00−33−330000000
χ392-22-2-122-221-12-21-2-2-1-1211-11-22-2-1100−2i2i−i3i3−i3i3i−ii−i-11-1100000000000−2i2i−i3i3−i3i3i−ii−i00−33−330000000
χ402-22-2-122-221-12-21-2-2-1-1211-11-22-2-1100−2i2ii3−i3i3−i3i−ii−i-11-1100000000000−2i2ii3−i3i3−i3i−ii−i003−33−30000000
χ412-2-22222-2-2-2-2-2-2222222-22-22-2-22-2-20000000000002-2-220000000000000000000002-22-2-220000000
χ422-2-22222-2-2-2-2-2-2222222-22-22-2-22-2-20000000000002-2-22000000000000000000000-22-222-20000000
χ432-2-22-122-2-211-2-2-122-1-121-11-1-2-221100003−3−333−3−33-111-100000000000003−3−333−3−33-221-1-110000000
χ442-2-22-122-2-211-2-2-122-1-121-11-1-2-221100003−3−33−333−3-111-100000000000003−3−33−333−32-2-111-10000000
χ452-2-22-122-2-211-2-2-122-1-121-11-1-2-22110000−333−33−3−33-111-10000000000000−333−33−3−332-2-111-10000000
χ462-2-22-122-2-211-2-2-122-1-121-11-1-2-22110000−333−3−333−3-111-10000000000000−333−3−333−3-221-1-110000000
χ4744444-2-2-2-244-2-24-2-2-2-21-2-2-2-2111-2-200000000000011114-2-2-2-211110000000000000000000000000
χ4844444-2-2-2-244-2-24-2-2-2-21-2-2-2-2111-2-20000000000001111-42222-1-1-1-10000000000000000000000000
χ494444-24-24-2-2-24-2-24-2-21-2-2-211-2-2-2-2100440000-2-2-2-2111100000000000-2-2000011110000000000000
χ504444-24-24-2-2-24-2-24-2-21-2-2-211-2-2-2-2100-4-400002222111100000000000220000-1-1-1-10000000000000
χ514444-2-24-24-2-2-24-2-241-2-211-2-2-2-2-21-24400-2-2-2-200001111000000000-2-200111100000000000000000
χ524444-2-24-24-2-2-24-2-241-2-211-2-2-2-2-21-2-4-4002222000011110000000002200-1-1-1-100000000000000000
χ5344-4-444-2424-4-4-2-4-424-2-24-422-222-4-2000000000000-2-2220000000000000000000000000000000000
χ5444-4-44-2-2-224-42-2-422-2-21-22221-1-12-200000000000011-1-10−2i32i300i3i3−i3−i30000000000000000000000000
χ5544-4-44-2-2-224-42-2-422-2-21-22221-1-12-200000000000011-1-102i3−2i300−i3−i3i3i30000000000000000000000000
χ5644-4-4-24-242-22-4-22-42-21-2-22-1-1-2222100000000−2i3−2i32i32i311-1-100000000000000000i3i3−i3−i30000000000000
χ5744-4-4-24-242-22-4-22-42-21-2-22-1-1-22221000000002i32i3−2i3−2i311-1-100000000000000000−i3−i3i3i30000000000000
χ5844-4-4-2-24-2-4-222422-41-2-21-122-222-1-24i−4i00−2i−2i2i2i000011-1-1000000000−2i2i00ii−i−i00000000000000000
χ5944-4-4-2-24-2-4-222422-41-2-21-122-222-1-2−4i4i002i2i−2i−2i000011-1-10000000002i−2i00−i−iii00000000000000000
χ604-44-44-2424-44-2-4-42-4-24-2224-42-22-2-4000000000000-22-220000000000000000000000000000000000
χ614-44-44-2-22-2-44-22-422-2-2122-22-11-1-220000000000001-11-1000−2i32i3i3−i3i3−i30000000000000000000000000
χ624-44-44-2-22-2-44-22-422-2-2122-22-11-1-220000000000001-11-10002i3−2i3−i3i3−i3i30000000000000000000000000
χ634-44-4-24-2-4-22-2422-42-21-2221-12-22-2-1004i−4i0000−2i2i−2i2i1-11-100000000000−2i2i0000i−ii−i0000000000000
χ644-44-4-24-2-4-22-2422-42-21-2221-12-22-2-100−4i4i00002i−2i2i−2i1-11-1000000000002i−2i0000−ii−ii0000000000000
χ654-44-4-2-24242-2-2-422-41-2-2-1-1-222-22120000−2i32i3−2i32i300001-11-10000000000000i3−i3i3−i300000000000000000
χ664-44-4-2-24242-2-2-422-41-2-2-1-1-222-221200002i3−2i32i3−2i300001-11-10000000000000−i3i3−i3i300000000000000000
χ674-4-4444-2-42-4-4-4244-24-2-2-442-222-2-42000000000000-222-20000000000000000000000000000000000
χ684-4-444-242-4-4-42-44-24-24-22-2-4422-22-4000000000000-222-20000000000000000000000000000000000
χ694-4-444-2-222-4-4224-2-2-2-212-22-2-1-11220000000000001-1-11000003-3-330000000000000000000000000
χ704-4-444-2-222-4-4224-2-2-2-212-22-2-1-11220000000000001-1-1100000-333-30000000000000000000000000
χ714-4-44-24-2-4222-42-24-2-21-22-2-1122-22-10000000023−23−23231-1-1100000000000000000−333−30000000000000
χ724-4-44-24-2-4222-42-24-2-21-22-2-1122-22-100000000−232323−231-1-11000000000000000003−3−330000000000000
χ734-4-44-2-242-4222-4-2-241-2-2-112-222-2-12000023−23−232300001-1-110000000000000−333−300000000000000000
χ744-4-44-2-242-4222-4-2-241-2-2-112-222-2-120000−232323−2300001-1-1100000000000003−3−3300000000000000000
χ758888-4-4-4-4-4-4-4-4-4-4-4-4222222222222000000000000-1-1-1-10000000000000000000000000000000000
χ7688-8-8-4-4-4-44-444-44442222-2-2-22-2-2-22000000000000-1-1110000000000000000000000000000000000
χ778-88-8-4-4-44-44-4-44444222-2-22-2-22-22-2000000000000-11-110000000000000000000000000000000000
χ788-8-88-4-4-4444444-4-4-4222-22-22-2-22-2-2000000000000-111-10000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).